Surface patch techniques for computational geometry

摘要

A method and system for computer aided design (CAD) is disclosed for designing geometric objects, wherein interpolation and/or blending between such objects is performed while deformation data is being input. Thus, a designer obtains immediate feedback to input modifications without separately entering a command(s) for performing such deformations. A novel N-sided surface generation technique is also disclosed herein to efficiently and accurately convert surfaces of high polynomial degree into a collection of lower degree surfaces. E.g., the N-sided surface generation technique disclosed herein subdivides parameter space objects (e.g., polygons) of seven or more sides into a collection of subpolygons, wherein each subpolygon has a reduced number of sides. More particularly, each subpolygon has 3 or 4 sides. The present disclosure is particularly useful for designing the shape of surfaces. Thus, the present disclosure is applicable to various design domains such as the design of, e.g., bottles, vehicles, and watercraft. Additionally, the present disclosure provides for efficient animation via repeatedly modifying surfaces of an animated object such as a representation of a face.

主权项

1. A method for decomposing a predetermined geometric surface into a plurality of geometric surface patches, comprising performing the following steps by computer equipment:
wherein a parametric domain for the predetermined geometric surface is divided into polygons, each of the polygons having less than five sides, wherein for a side of each polygon, there is a corresponding object space boundary curve provided to approximate a corresponding portion of the predetermined geometric surface, the object space boundary curve being for one of the plurality of geometric surface patches for approximating the predetermined geometric surface, the object space boundary curve having the side as a domain therefor, and each point, P, of the object space boundary curve represented as a corresponding weighted sum, having weights therefor, such that (a) through (c) below are satisfied: (a) there is a first term of the corresponding weighted sum, wherein the first term includes a product of: (i) a point L on a first tangent to the object space boundary curve at a first end point of the object space boundary curve, and (ii) a first of the weights of the corresponding weighted sum for P, wherein the point L and the first weight is determined according to a function having a domain space whose values also identify points of the side for the object space boundary curve, and the function monotonically varies between a predetermined first value and a predetermined second value, the predetermined first value less than the predetermined second value; wherein the first tangent is a line or vector that is tangent to the object space boundary curve along a length thereof at the first end point; (b) there is a second term of the corresponding weighted sum, wherein second term includes a product of: (i) a point Ri on a second tangent to the object space boundary curve at a second end point of the object space boundary curve, and (ii) a second of the weights of the corresponding weighted sum for P, wherein the point Ri and the second weight is determined according to the function; wherein the second tangent is a line or vector that is tangent to the object space boundary curve along a length thereof at the second end point; wherein for the point P of the object space boundary curve, the weights of the corresponding weighted sum, include the first and second weights, and the first and second weights sum to one and each of the first and second weights is in a range of zero and one; (c) each point on the object space boundary curve is within a predetermined tolerance of the predetermined geometric surface; generating, for each of the polygons Pj, a corresponding one of the geometric surface patches Sj having the polygon Pj as the domain for the corresponding one geometric surface patch Sj, wherein the object space boundary curve for the polygon Pj is included in the boundary of Sj, and each interior point of Sj: (1) has is a corresponding interior point of the polygon Pj, and (2) is a weighted sum of boundary points of Sj wherein each weight (WT) of the weighted sum of boundary points of Sj is a product of weight terms wherein each weight term is dependent upon a distance value of the of the corresponding point from a side of the polygon Pj; wherein the predetermined geometric surface is represented by a parametric polynomial of at least a particular degree, and each of the plurality of geometric surface patches is represented by a corresponding polynomial of lower degree than the particular degree; wherein each geometric surface patch Sj conforms to a corresponding portion of the predetermined geometric surface so that there is no more than a desired amount of error between the predetermined geometric surface and the plurality of geometric surface patches; and for the polygons, individually identified as Pj, a step of using their corresponding geometric surface patches Sj, in place of the predetermined geometric surface, for obtaining a design or shape of an article of manufacture or for modeling of a process or physical feature.